The present invention discloses a composition for use in a method of alleviating pain which comprises administering to a mammal exhibiting pain (a) an analgesia-inducing amount of a non-narcotic analgesic such as an NSAID coxibs and (b) an analgesia enhancing amount of at least one analgesia enhancer. Furthermore, the therapeutic composition is applicable to the treatment of all varieties of pain and not just those associated with inflammation, pain as in the prior art.